Jason, as Mike Drew suggested above, when I saw the question I frankly wasn't interested to either just comment that the difference was almost certainly insignificant or to research for an authority to lend some weight to that view. Since you've taken the time to find that good Audire explanation(which I hadn't seen before), I decided to try to retrieve some of the stuff that I'd seen in the past. One thing that stuck in my mind was
this discussion by physicist and speaker designer John Murphy taken from some of his posts on an audio discussion group. Scrolling down to the June 2, 1999 post, his concept of relating the amount of group delay that might be audible to how many "cycles" it equated to at very low subwoofer frequencies seems quite powerful and the one cycle threshold for audibility that he proposed seems reasonable. As shown in his example there involving the ACI driver, the amount of group delay for even the vented system was well under one cycle. The difference between the vented and closed enclosures was still smaller of course, and even less likely to be audible. So, my view(not that I've spent much time pondering the question)has been that this isn't of real-world significance.
As to the "orders" of the various enclosure types, the significance lies in how rapidly the response rolls off below the tuned frequency, which is quite important(and how the group delay at the lower frequencies increases in proportion to the steepness of the rolloff, apparently not very important). The rolloff is 6dB per octave per "order", e.g., a closed enclosure said to be 2nd order rolls off at 12dB per octave, a vented 4th order enclosure rolls off at 24db per octave.The way the numbering of the orders arises is through the analogy to electrical(rather than acoustical)crossovers which also create rolloffs. A first order crossover contains basically just one element(a capacitor in series with the tweeter, an inductor with the woofer)per driver and rolls it off at 6db/octave above(woofer)or below(tweeter)the selected crossover frequency. As more elements are added to the crossover to increase the steepness of the rolloff, the number of elements determines the order of the crossover; e.g., in a second order crossover both an inductor and capacitor are used for each driver, series capacitor and parallel inductor to the tweeter, series inductor and parallel capacitor to the woofer, resulting in a 12dB/octave rolloff. As more elements are added there can be 3rd order, 4th order, etc. crossovers with proportionally steeper rolloffs but also higher power losses in the crossover.
